Mecanique Analytique 2021/2022

Emploi du temps

Dimanche: 10h30mn-11h30mn (Cours)

Dimanche: 12h30mn-13h30mn (Cours)

Lundi(G1): 12h30mn-13h30mn (TD)

Mardi(G2): 12h30mn-13h30mn (TD)


Herbert Goldstein, Classical Mechanics.

Walter Greiner, Classical Mechanics: System of Particles and Hamiltonian Dynamics.

Landau and Lifshitz, Mechanics.

En Francais:

Amiot et Marleau, Mecanique Analytique

En Arabe:

Badis Ydri, Fundamental Physics



Equations de Lagrange et formalism Lagrangien virtuel (particules ponctuelles, symmetries et principes de conservation, degre de liberte, contraintes holonomes, coordonnees generalisees, espace de configuration, principe de travail virtuel, Lagrangien, calcul variationnel, principe de moindre action d'Hamilton, theorem de Noether, invariance de jauge).


Equations de  Hamilton et formalism Hamiltonien canonique (lois de conservation et constantes du mouvement, transformations de Legendre, Hamiltonien, moment generalise,espace de phase,  equations de Hamilton, transformations canoniques, forme symplectique, crochets de Poisson, theorem de Liouville, equation d'Hamilton-Jacobi,).

Applications physiques (chute libre, probleme a deux corps et force centrale, rotation de corps solide, oscillation simple et theorie des perturbations, electrodynamique classique, relativite restreinte et espace-temps, chaos et mecanique non-lineaire, mecanique numerique, cosmologie, theorie des champs).   




Bell's theorem: A bridge between the measurement and the mind/body problems


In this essay a quantum-dualistic, perspectival and synchronistic interpretation of quantum mechanics is further developed in which the classical world-from-decoherence which is perceived (decoherence) and the perceived world-in-consciousness which is classical (collapse) are not necessarily identified. Thus, Quantum Reality or "{\it unus mundus}" is seen as both i) a physical non-perspectival causal Reality where the quantum-to-classical transition is operated by decoherence, and as ii) a quantum linear superposition of all classical psycho-physical perspectival Realities which are governed by synchronicity as well as causality (corresponding to classical first-person observes who actually populate the world). This interpretation is termed the Nietzsche-Jung-Pauli interpretation and is a re-imagining of the Wigner-von Neumann interpretation which is also consistent with some reading of Bohr's quantum philosophy.  

Comments: This essay is a summary of the main ideas found in the book (Philosophy and the Interpretation of Quantum Physics) published in 2021 with Institute of Physics (IOP) here this https URL. The essays arXiv:2008.09500 [hep-th], arXiv:2007.04489 [physics.hist-ph] and arXiv:1811.04245 [quant-ph] contain further discussion of other related ideas found in the book.


Subjects: History and Philosophy of Physics (physics.hist-ph); Quantum Physics (quant-ph).

Quantized Noncommutative Geometry from Multitrace Matrix Models


In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is proposed in which noncommutative geometry can emerge from "one-matrix multitrace scalar matrix models" by probing the statistical physics of commutative phases of matter. This is in contrast to the usual mechanism in which noncommutative geometry emerges from "many-matrix singletrace Yang-Mills matrix models" by probing the statistical physics of noncommutative phases of gauge theory. In this novel scenario quantized geometry emerges in the form of a transition between the two phase diagrams of the real quartic matrix model and the noncommutative scalar phi-four field theory. More precisely, emergence of the geometry is identified here with the emergence of the uniform-ordered phase and the corresponding commutative (Ising) and noncommutative (stripe) coexistence lines. The critical exponents and the Wigner's semicircle law are used to determine the dimension and the metric respectively. Arguments from the saddle point equation, from Monte Carlo simulation and from the matrix renormalization group equation are provided in support of this scenario.  

Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Lattice (hep-lat)

On the AdS/CFT correspondence and quantum entanglement 


String theory provides one of the most deepest insights into quantum gravity. Its single most central and profound result is the gauge/gravity duality, i.e. the emergence of gravity from gauge theory. The two examples of M(atrix)-theory and the AdS/CFT correspondence, together with the fundamental phenomena of quantum entanglement, are of paramount importance to many fundamental problems including the physics of black holes (in particular to the information loss paradox), the emergence of spacetime geometry and to the problem of the reconciliation of general relativity and quantum mechanics. In this article an account of the AdS/CFT correspondence and the role of quantum entanglement in the emergence of spacetime geometry using strictly the language of quantum field theory is put forward.  


Appeared under the title (The AdS/CFT correspondence) as the final chapter of the second volume of the book (A Modern Course in Quantum Field Theory) published with Institute of Physics (IOP) in 2019. Volume 1: this https URL. Volume 2: this https URL  Subjects:                 

    High Energy Physics - Theory (hep-th); High Energy Physics - Experiment (hep-ex); High Energy Physics - Lattice (hep-lat); High Energy Physics - Phenomenology (hep-ph)